Wyniki wyszukiwania - BazTech

Ograniczanie wyników

1 Fundamenta Informaticae

1 2022

Powiadomienia systemowe

Sesja wygasła!
Sesja wygasła!
Sesja wygasła!

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: local antimagic labeling

Sortuj według:

Ogranicz wyniki do:

On Local Antimagic Vertex Coloring for Complete Full t-ary Trees.

Bača Martin, Semaničová-Feňovčíková Andrea

Fundamenta Informaticae

2022

Vol. 185, nr 2

99--113

Let G = (V, E) be a finite simple undirected graph without K2 components. A bijection f : E → {1, 2, ⋯, |E|} is called a local antimagic labeling if for any two adjacent vertices u and v, they have different vertex sums, i.e., w(u) ≠ w(v), where the vertex sum w(u) = ∑e∈E(u)f(e), and E(u) is the set of edges incident to u. Thus any local antimagic labeling induces a proper vertex coloring of G where the vertex v is assigned the color (vertex sum) w(v). The local antimagic chromatic number χla(G) is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. It was conjectured [6] that for every tree T the local antimagic chromatic number l + 1 ≤ χla(T) ≤ l + 2, where l is the number of leaves of T. In this article we verify the above conjecture for complete full t-ary trees, for t ≥ 2. A complete full t-ary tree is a rooted tree in which all nodes have exactly t children except leaves and every leaf is of the same depth. In particular we obtain that the exact value for the local antimagic chromatic number of all complete full t-ary trees is l + 1 for odd t.